I have a 2001 Gl1800 with 106,600 miles on it. I can't get the neutral light to stay on when I shift into neutral. Actually, it will stay on occasionally, but usually it just gives a brief flash and goes out when I shift up to neutral from first, or down from second. I suspect the problem is with the gear position switch. Has anyone else had this problem and if so, how did you solve it.

Found something similar when I had a 2001 wing. I removed the selector arm and cleaned all the excess crap that had gathered behind it (this then caused a slight leak so replaced the bearing on the selector shaft) then never any problem with selecting neutral. Hope yours is as easy.

The problem with mine turned out to be the gear position switch which is in the shift linkage cover which is located on the front of the engine, below the timing chain cover. I found a cover and switch on ebay and found it easier to replace my old cover/switch with the ebay parts (the gasket on the cover is a bear to get off). The switch connector is located under the air intake box, which means everything must be removed right down to the throttle bodies (quite a lengthy job). While you're at it, you might as well replace the air filter. Now everything works as it should. The engineers at Honda could have made this job much easier if they had moved the connector down on the front of the engine. Actually, now that I've done this once, if I ever have to make this repair again I will splice the wires of the new switch onto the existing wires of the old switch. This would save about a day's work when you consider all the stuff that has to be dealt with.
rstoops1